Tests of Universality of Baryon Form Factors In Holographic QCD
A. Cherman, T.D. Cohen, M. Nielsen, PRL103(09) Univ. of Maryland and Univ. of Sao Paulo
Low x Meeting, September 2009 QCD: strong-coupled theory AdS/QCD models: successful at reproducing low energy hadronic observables
• two classes of AdS/QCD models
Top-down models: Botton-up models:
arise from sting theory QCD large Nc dual to a classical 5D theory D4/D8 system gauge theory confining as QCD field content 5D matched
AdS/CFT requires large Nc to low energy chiral and ´t Hooft coupling symmetry of QCD Both cases: large Nc is required
QCD is a weakly-interacting theory of long -lived mesons in the • ‘t Hooft, 1973 large Nc limit.
• In the large Nc limit, baryons are ‘soliton -like’ configurations of meson fields. Witten, 1979 1 • Baryon masses scale as Nc (composed of Nc quarks), 1/2 interactions with mesons scale as Nc .
• Unlike mesons, baryons are not narrow at large Nc. • Nucleons, deltas, become degenerate. Mass splitting -1 scales as Nc . • In contrast to the pure meson sector, meson loops make leading order contributions to baryon properties at large Nc.
• Variety of baryon models (Skyrme models) use large Nc properties of baryons for inspiration. Skyrme, 1961 • Baryons modeled as quantum states of slowly rotating Adkins, Nappi, hedgehog Skyrmions of meson fields. Witten, 1983 Dashen, Manohar, Jenkins,1993-95 Model-independent relations for baryons
valid at large Nc • Goldberger-Treiman relation: • Relation is model-indepedent, and follows from chiral symmetry. • Nucleon and delta couplings with pions are related by • • This relation follows just from the large Nc limit • New model-independent relation: • Ratio of nucleon form factors in position space, evaluated at large distances:
• Relation depends on both the large Nc and chiral limits. • Can serve as a useful and highly non -trivial probe of large Nc baryon models. Model independence of the ratio
Leading large r behavior of form factors in large Nc ChiPT are mediated by pions
Three pion interaction - comes from anomaly.
Two pion interaction. • In the large Nc limit, leading contributions to isovector electric and isoscalar magnetic form factors are sensitive to the nucleon - delta mass splitting ~ 1/N c (Cohen PLB 359)
ratio is independent of Skyrme-type models
SU(2) matrix
• Original Skyrme model includes only pion fields. • Baryons appear as quantum states of slowly rotating hedgehog Skyrmions of pion fields. hedgehog ansatz:
in the large r limite f(r) goes like in the Skyrme model: 5D Skyrmions
Pomarol-Wulzer holographic baryon model
Pomarol, Wulzer, NPB809:347 -361,2009.
Panico, Wulzer, arXiv:0811.2211
• Bottom-up AdS /QCD model: uses hard -wall AdS background, with two U(2) 5D gauge fields, L M RM, associated with 4D left and right quark currents ( AdS /CFT dictionary). • Chiral symmetry broken by choice of IR boundary conditions for 5D gauge fields. • Has a 5D CS term to get anomaly physics right. • this model looks quite different from 4D Skyrme models: there are no explicit pion fields. • Baryons appear as quantum states of slowly rotating Skyrmion-like hedgehog configurations of the 5D gauge field. • Skyrmions are stabilized by the CS term. gA = 0.65 in the original Skyrme model in the large r limit
large Nc and chiral physics handled correctly in Pomarol-Wulzer model
Baryons as Holographic Instantons Sakai-Sugimoto model
Hata et al, hep -th/0701280
Hashimoto, Sakai, Sugimoto, PTP120:1093-1137,2008
• Top-down AdS/QCD model: baryons are described as instantons in a 5D Yang-Mills and CS theory, formulated in the D4/D8 model.
• AM :5D U( Nf) field, FMN : field strength, CS 5 -form
• Model expected to make sense when Nc and the ‘t Hooft coupling are large. • CS term stabilizes the instanton size to be of order • At large higher derivative terms are not suppressed, and 1/ expansion is not well justified
SS in the large r limit
related with meson rho mass • Model does not satisfy large Nc relation. • Ratio depends on model parameters. • Model fails because it does not treat chiral symmetry correctly. • Another signal: the isovector charge radius is finite in the model. It is known to be infinite in chiral perturbation theory in the chiral limit. • These results suggest that the Sakai -Sugimoto instanton model fails to correctly describe the long-range part of large Nc baryon physics. Summary • We discussed a model -independent large Nc relation for baryons.
• Relation probes consistency of implementation of chiral and large Nc physics in baryon models. • In this case, the probe reveals that some holographic models get large Nc chiral physics right, while others do not.
• This situation illustrates the utility of large Nc analysis as a diagnostic tool for probing models.
• Relation should be checked in other new large Nc baryon models. http://www.sbf1.sbfisica.org.br/eventos/extras/hadrons2010/
XI HADRON PHYSICS March, 22 - 27, 2010, São Sebastião, Brazil origem of problem: large expansion. • SS model: pion nucleon coupling scales as
• pion loops contributions to nucleon properties are discarded if the large limit is taken prior to the
large Nc limit. • It is necessary to go beyond large limit in the SS
model to capture large Nc chiral physics. Definitions
These position-space form factors can be related to the standard (experimentally accessible) momentum -space form factors by the appropriate Fourier transforms.